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Most Important Selected Qs for JEE AdvancedMathematicsParabola

Let y^2=x be a given parabola and a variable chord cuts the parabola at P and Q . Let C be the vertex of parabola. If the locus of the point of intersection of tangents at P and Q is x+1=0 , then the minimum area of triangle P C Q be M . Find 4 M .

Correct answer

4

Step-by-step solution

aligned a t₁ t₂ & =-1 t₁ t₂= -1 a =-4 & = 1 2 | array ccc 0 & 0 & 1 a t₁^2 & 2 a t₁ & 1 a t₂^2 & 2 a t₂ & 1 array |= 1 2 (2 a^2 t₁^2 t₂-2 a^2 t₁ t₂^2 ) & = |a^2 t₁ t₂ (t₁-t₂ ) |= 1 4 |t₁-t₂ | & = 1 4 (t₁+ 4 t₁ )= 1 4 [ ( t₁ - 2 t₁ )^2+4 ] _ . & =1=M 4 M & =4 aligned

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